I am trying to find the modern pinyin and characters for a scientist called Shu Chang-Yui, http://www.internationalstory.gla.ac.uk/person/?id=WH24481 so that I can type up some information about him in Chinese, but I cannot find anything with this version of his name.

It's Mandarin, just not in Pinyin because Pinyin didn't exist at the time the man first had to write his name in latin letters in his documents.

With a bit of guesswork as to what his surename might be, google told me his name is 舒昌譽 (Shū Chàngyù in Pinyin) or in simplified characters 舒昌誉. If you want my exact source, he is mentioned in the last paragraph of page 99 in this book (https://books.google.de/books?id=jb17BgAAQBAJ&pg=PA99&lpg=PA99&dq=%E8%88%92%E6%98%8C%E8%AD%BD&source=bl&ots=hknnEshgGB&sig=QtvHU6SJMV7zXNPkzPk496tgz4E&hl=de&sa=X&redir_esc=y#v=onepage&q&f=false).